S2T2

Jim Randell 11:58 am on 30 July 2019 Permalink Reply
Tags: by: G H Dickson ( 13 )   

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  Jim Randell 11:58 am on 30 July 2019 Permalink | Reply

  This Python program runs in 410ms.

  Run: [ @repl.it ]

  from enigma import (irange, subsets, multiset, cproduct, printf)
  
  # find sets of 5 scores that sum to 100
  ss = list()
  for s in subsets(irange(11, 40), size=5, select='C'):
    # total score is 100
    if not (sum(s) == 100): continue
    # (best + 3rd best) = (6/5)(best + 4th best)
    if not (5 * (s[-1] + s[-3]) == 6 * (s[-1] + s[-4])): continue
    ss.append(s)
  
  # choose scores for the 3 students
  for (s1, x2, x3) in subsets(ss, size=3, select='C'):
    # choose orders for s2 and s3
    permute = lambda x: subsets(x, size=len, select='P')
    for (s2, s3) in cproduct([permute(x2), permute(x3)]):
      scores = (s1, s2, s3)
      # accumulate the total scores in each test
      ts = list(sum(s) for s in zip(*scores))
      m = multiset(ts)
      if not (sorted(m.values()) == [1, 4]): continue
      # find the highest and second highest marks
      ms = sorted(s1 + s2 + s3)
      (m1, m2, m3) = (ms[-1], ms[-2], ms[-3])
      if not (m1 > m2 > m3): continue
  
      # determine which is Tom, Dick
      T = D = H = -1
      for (i, s) in enumerate(scores):
        if m1 in s: T = i
        if m2 in s: D = i
      # Harry is the other one
      H = 3 - (T + D)
      if not (sorted([T, D, H]) == [0, 1, 2]): continue
      # check the 2nd highest score is in the test with the unique total
      d = scores[D].index(m2)
      if not (m[ts[d]] == 1): continue
  
      # output solution
      printf("T = {T}", T=scores[T])
      printf("D = {D}", D=scores[D])
      printf("H = {H}", H=scores[H])
      printf("+ = {ts}")
      printf("answer = {x}", x=scores[H][d])
      printf()
  

  Solution: 15 marks.

  The scores in each test are shown below:

  

  The highest single mark is highlighted red. The second highest mark is orange. And the answer (Harry’s mark in the same subject as the second highest mark) is yellow.

  There is a “near miss” scenario, where the scores are as follows:

  T = (11, 12, 21, 23, 33)
  D = (25, 26, 22, 14, 13)
  H = (25, 23, 13, 24, 15)

  The sum of the scores for each test are 61, apart from the third one where they are 56.

  Tom has the highest score (33) and Dick has the second highest (26), but the score of 26 is not in the subject with a sum of 56.

  The scores are a rearrangement of the scores in the actual solution because there are only three possible sequences of 5 scores between 11 and 40 that sum to 100 and have best and third best scores summing to one fifth more than the sum of the best and fourth best scores.

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